Question

Expand the following, using suitable identities: ${(2x-y+z)}^2$

Answer 1

Expansion of ${(2x–y+z)}^2$

Using identity,

${\mathbf{(}\mathit{a}\mathbf{}\mathbf{+}\mathbf{}\mathit{b}\mathbf{}\mathbf{+}\mathbf{}\mathit{c}\mathbf{)}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}{\mathit{a}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}{\mathit{b}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}{\mathit{c}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}\mathit{a}\mathit{b}\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}\mathit{b}\mathit{c}\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}\mathit{c}\mathit{a}$

Here,

$$\begin{gathered} {(2x–y+z)}^2=(2x{)}^2+{(-y)}^2+z^2+(2\times 2x\times -y)+(2\times -y\times z)+(2\times z\times 2x) \\ =4x^2+y^2+z^2–4xy–2yz+4xz \end{gathered}$$

Hence, expansion of ${(2x-y+z)}^2=4x^2+y^2+z^2–4xy–2yz+4xz$